All Stable Characteristic Classes of Homological Vector Fields

An odd vector field $Q$ on a supermanifold $M$ is called homological, if $Q^2=0$. The operator of Lie derivative $L_Q$ makes the algebra of smooth tensor fields on $M$ into a differential tensor algebra. In this paper, we give a complete classification of certain invariants of homological vector fields called characteristic classes. These take values in the cohomology of the operator $L_Q$ and are represented by $Q$-invariant tensors made up of the homological vector field and a symmetric connection on $M$ by means of tensor operations.Comment: 17 pages, references and comments adde

A quantitative comparison of in-line coating thickness distributions obtained from a pharmaceutical tablet mixing process using discrete element method and terahertz pulsed imaging

The application of terahertz pulsed imaging (TPI) in the in-line configuration to monitor the coating thickness distribution of pharmaceutical tablets has the potential to improve the performance and quality of the spray coating process. In this study, an in-line TPI method is used to measure coating thickness distributions on pre-coated tablets during mixing in a rotating pan, and compared with results obtained numerically using the discrete element method (DEM) combined with a ray-tracing technique. The hit rates (i.e. the number of successful coating thickness measurements per minute) obtained from both terahertz in-line experiments and the DEM/ray-tracing simulations are in good agreement, and both increase with the number of baffles in the mixing pan. We demonstrate that the coating thickness variability as determined from the ray-traced data and the terahertz in-line measurements represents mainly the intra-tablet variability due to relatively uniform mean coating thickness across tablets. The mean coating thickness of the ray-traced data from the numerical simulations agrees well with the mean coating thickness as determined by the off-line TPI measurements. The mean coating thickness of in-line TPI measurements is slightly higher than that of off-line measurements. This discrepancy can be corrected based on the cap-to-band surface area ratio of the tablet and the cap-to-band sampling ratio obtained from ray-tracing simulations: the corrected mean coating thickness of the in-line TPI measurements shows a better agreement with that of off-line measurements

Quaternary structure of the European spiny lobster (Palinurus elephas) 1 x 6-mer hemocyanin from cryoEM and amino acid sequence data

Arthropod hemocyanins are large respiratory proteins that are composed of up to 48 subunits (8 x 6-mer) in the 75 kDa range. A 3D reconstruction of the 1 x 6-mer hemocyanin from the European spiny lobster Palinuris elephas has been performed from 9970 single particles using cryoelectron microscopy. An 8 Angstrom resolution of the hemocyanin 3D reconstruction has been obtained from about 600 final class averages. Visualisation of structural elements such as a-helices has been achieved. An amino acid sequence alignment shows the high sequence identity (>80%.) of the hemocyanin subunits from the European spiny lobster P. elephas and the American spiny lobster Panulirus interruptus. Comparison of the P. elephas hemocyanin electron microscopy (EM) density map with the known P. interruptus X-ray structure shows a close structural correlation, demonstrating the reliability of both methods for reconstructing proteins, By molecular modelling, we have found the putative locations for the amino acid sequence (597-605) and the C-terminal end (654-657), which are absent in the available P. interruptus X-ray data. (C) 2002 Elsevier Science Ltd. All rights reserve

Development of 3D printed rapid tooling for micro-injection moulding

The use of additive manufacturing techniques in conjunction with injection moulding is becoming increasingly popular, with financial and time benefits to coupling the techniques. This study demonstrates a systematic development process of 3D printed rapid tooled moulds using stereolithography. A high flexural modulus and elongation were found to increase the likelihood of success of a mould material in the injection moulding process. Success is defined as the mould surviving the process and being capable of producing the desired object successfully. Stereolithography was found to produce high quality moulds when a diagonal print orientation and a scaling factor of 109.3% is employed. The presented technique and systematic workflow is highly suitable for the production of moulds with detailed micro-features. This is of particular interest for rapid tooling for micro-injection moulding for the manufacture of pharmaceuticals and medical devices, where the microstructure directly impacts the performance of the products

A predictive integrated framework based on the radial basis function for the modelling of the flow of pharmaceutical powders

This study presents a modelling framework to predict the flowability of various commonly used pharmaceutical powders and their blends. The flowability models were trained and validated on 86 samples including single components and binary mixtures. Two modelling paradigms based on artificial intelligence (AI) namely, a radial basis function (RBF) and an integrated network were employed to model the flowability represented by the flow function coefficient (FFC) and the bulk density (RHOB). Both approaches were utilized to map the input parameters (i.e. particle size, shape descriptors and material type) to the flow properties. The input parameters of the blends were determined from the particle size, shape and material type properties of the single components. The results clearly indicated that the integrated network outperformed the single RBF network in terms of the predictive performance and the generalization capabilities. For the integrated network, the coefficient of determination of the testing data set (not used for training the model) for FFC was R2=0.93, reflecting an acceptable predictive power of this model. Since the flowability of the blends can be predicted from single component size and shape descriptors, the integrated network can assist formulators in selecting excipients and their blend concentrations to improve flowability with minimal experimental effort and material resulting in the (i) minimization of the time required, (ii) exploration and examination of the design space, and (iii) minimization of material waste

Multi-modal dissolution testing system for pharmaceutical tablets

This project aims to develop a novel multimodal sensor system that is capable of resolving the key processes, as well as how these processes are linked to microstructure, formulation and raw material attributes

Quantum Open-Closed Homotopy Algebra and String Field Theory

We reformulate the algebraic structure of Zwiebach's quantum open-closed string field theory in terms of homotopy algebras. We call it the quantum open-closed homotopy algebra (QOCHA) which is the generalization of the open-closed homotopy algebra (OCHA) of Kajiura and Stasheff. The homotopy formulation reveals new insights about deformations of open string field theory by closed string backgrounds. In particular, deformations by Maurer Cartan elements of the quantum closed homotopy algebra define consistent quantum open string field theories.Comment: 36 pages, fixed typos and small clarifications adde

The partially alternating ternary sum in an associative dialgebra

The alternating ternary sum in an associative algebra, $abc - acb - bac + bca + cab - cba$, gives rise to the partially alternating ternary sum in an associative dialgebra with products $\dashv$ and $\vdash$ by making the argument $a$ the center of each term: $a \dashv b \dashv c - a \dashv c \dashv b - b \vdash a \dashv c + c \vdash a \dashv b + b \vdash c \vdash a - c \vdash b \vdash a$. We use computer algebra to determine the polynomial identities in degree $\le 9$ satisfied by this new trilinear operation. In degrees 3 and 5 we obtain $[a,b,c] + [a,c,b] \equiv 0$ and $[a,[b,c,d],e] + [a,[c,b,d],e] \equiv 0$; these identities define a new variety of partially alternating ternary algebras. We show that there is a 49-dimensional space of multilinear identities in degree 7, and we find equivalent nonlinear identities. We use the representation theory of the symmetric group to show that there are no new identities in degree 9.Comment: 14 page

QuickSel: Quick Selectivity Learning with Mixture Models

Estimating the selectivity of a query is a key step in almost any cost-based query optimizer. Most of today's databases rely on histograms or samples that are periodically refreshed by re-scanning the data as the underlying data changes. Since frequent scans are costly, these statistics are often stale and lead to poor selectivity estimates. As an alternative to scans, query-driven histograms have been proposed, which refine the histograms based on the actual selectivities of the observed queries. Unfortunately, these approaches are either too costly to use in practice---i.e., require an exponential number of buckets---or quickly lose their advantage as they observe more queries. In this paper, we propose a selectivity learning framework, called QuickSel, which falls into the query-driven paradigm but does not use histograms. Instead, it builds an internal model of the underlying data, which can be refined significantly faster (e.g., only 1.9 milliseconds for 300 queries). This fast refinement allows QuickSel to continuously learn from each query and yield increasingly more accurate selectivity estimates over time. Unlike query-driven histograms, QuickSel relies on a mixture model and a new optimization algorithm for training its model. Our extensive experiments on two real-world datasets confirm that, given the same target accuracy, QuickSel is 34.0x-179.4x faster than state-of-the-art query-driven histograms, including ISOMER and STHoles. Further, given the same space budget, QuickSel is 26.8%-91.8% more accurate than periodically-updated histograms and samples, respectively